Triangular-hexagonal duoprismatic prism
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Triangular-hexagonal duoprismatic prism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Trahip |
Coxeter diagram | x x3o x6o |
Elements | |
Tera | 6 triangular-square duoprisms, 2 triangular-hexagonal duoprisms, 3 square-hexagonal duoprisms |
Cells | 6+12 triangular prisms, 18 cubes, 3+6 hexagonal prisms |
Faces | 12 triangles, 18+18+36 squares, 6 hexagons |
Edges | 18+36+36 |
Vertices | 36 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths 1 (disphenoid base 1), √3 (disphenoid base 2), √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tisdip–trip–tisdip: 120° |
Thiddip–trip–tisdip: 90° | |
Shiddip–cube–tisdip: 90° | |
Thiddip–hip–shiddip: 90° | |
Shiddip–hip–shiddip: 60° | |
Heights | Thiddip atop thiddip: 1 |
Hip atop shiddip: | |
Central density | 1 |
Number of external pieces | 11 |
Level of complexity | 30 |
Related polytopes | |
Army | Trahip |
Regiment | Trahip |
Dual | Triangular-hexagonal duotegmatic tegum |
Conjugate | Triangular-hexagonal duoprismatic prism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A2×G2×A1, order 144 |
Convex | Yes |
Nature | Tame |
The triangular-hexagonal duoprismatic prism or trahip, also known as the triangular-hexagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-hexagonal duoprisms, 3 square-hexagonal duoprisms, and 6 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-hexagonal duoprisms, and 1 triangular-hexagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a triangular-hexagonal duoprismatic prism of edge length 1 are given by:
Representations[edit | edit source]
A triangular-pentagonal duoprismatic prism has the following Coxeter diagrams:
- x x3o x6o (full symmetry)
- x x3o x3x (hexagons as ditrigons)
- xx3oo xx6oo&#x (triangular-hexagonal duoprism atop triangular-hexagonal duoprism)
- xx3oo xx3xx&#x
- ox xx xx6oo&#x (hexagonal prism atop square-hexagonal duoprism)
- ox xx xx3xx&#x
- xxx xxx3xxx&#x
External links[edit | edit source]
- Klitzing, Richard. "trahip".